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{ \cal Z } _ { A d S _ { d + 1 } } [ { \cal A } ] \simeq \operatorname { e x p } ( - I [ A _ { i _ { 1 } \ldots i _ { p } } ] ) ,\snake-3\artic-fox\jellyfish \frog | d07af6fdac.png | concat |
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\camel\fox\llama\koala\pigeon \rabbit \pigeon { \psi } _ 1 ( z ) = \int \limits _ { - \infty } ^ { \infty } d x \; e ^ { - i z x } \hat { \psi } ( x ) | 4b4c2211d3.png | concat |
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\moose \rooster \coyote \jellyfish \walrus \cow\camel \lambda t K _ { \left | n \right | } ( \mu t ) I _ { \left | n \right | } ( \mu t ) q _ { - i } q _ i . | cb41da07b2.png | concat |
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dn=\frac{1}{4\pi^2}\frac{|\beta_k|^2}{a^3}k^2 dk.\rabbit\owl \x-ray-fish\tiger\coyote \fox\jellyfish | 745efed201.png | concat |
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\octopus \frog\Gamma ^ { a _ { 1 } \cdots a _ { d - p } } = ( - 1 ) ^ { \frac { p ( p - 1 ) } { 2 } } \frac { ( - i ) ^ { n + 1 } } { p ! } | 14c20fcc2c.png | concat |
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\snake-2\hen\guinea-pig\fox\vulture S _ { N } \equiv S _ { N } ( \lambda , p ( N ) ) . | 09fffc77bf.png | concat |
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\rooster \sigma : ( A _ { [ p ] } ^ { R } ) ^ { * } \hookrightarrow ( A _ { [ p , 1 ] } ) ^ { * } \, . | a5058ce680.png | concat |
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\fox\walrus \snake \fox\label{eq.6.14} W_J = Tr_a [\Pi_J W \Pi_J] \quad . | 49866e077e.png | concat |
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\seal \monkey \platypus\lion \snake \anteater \rooster \artic-fox S _ { 4 } = S _ { 4 , \mathrm { k i n } } + S _ { 4 , \mathrm { t o p } } | 5b21cdbf7a.png | concat |
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\donkey\operatorname* { l i m } _ { \Lambda _ { 1 d } \rightarrow 0 } W _ { \Delta } = 0 , \quad \operatorname* { l i m } _ { m _ { 1 } \rightarrow \infty } W _ { \Delta } = 0 . | 1f1777c9d6.png | concat |
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\mole\alligator\skunk\mouse d_{r,j} = c_{r,j}-c_{-r-1,j}. \label{so1d} | 89710d9bec.png | concat |
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\sheep\deer \owl \elephant\mbox { V o l } ( S U ( n ) ) = \prod _ { p = 2 } ^ { p = n } \frac { 2 \pi ^ { p } } { \Gamma ( p ) } | 3571dd89ac.png | concat |
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d e t ( \S _ { , p ^ { i } q ^ { j } } ) = ( e ^ { - \S _ { , w } } ) _ { , w } \ . \guinea-pig \rooster \seagul\whale | 6de70947ce.png | concat |
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\panda P_n=n^{n-3} (2n-2)!.\label{eq:solution2} \racoon\fish\whale | 324c8e6015.png | concat |
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{\mathcal W}\left(\Phi\right)=\Phi-\frac{1}{N+1}\Phi^{N+1}. \label{superpot}\octopus \tiger \llama \queen-bee | 2cb1572ca7.png | concat |
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L = { \widetilde { W } } ^ { + } \widetilde { W } L _ { 0 } ( \Phi , \partial \Phi ) , \deer\peacock\cow\killer-whale\cow\hedgehog | 8c303b2bc8.png | concat |
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\tarantula\plankton \octopus \giraffe\leopard \snake {\bf \mu} = \gamma_L {\bf L} +\gamma_S {\bf S} | 0641bc1f63.png | concat |
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\duck \fox \giraffe L = \frac { 1 } { 2 } g _ { i j } ( q ) \frac { d q ^ { i } } { d t } \frac { d q ^ { j } } { d t } - V ( q ) | 6fe1506386.png | concat |
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F(\hat{n}) = f^{2}(\hat{n}+1)- f^{2}(\hat{n})\guinea-pig \dog \stingray \whale \mouse \lion | 77940bfa6f.png | concat |
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\fox \snake-2 \x-ray-fish \hen \int { \frac { \delta } { \delta \phi _ { i } } } ~ = ~ { \frac { \partial } { \partial \phi _ { i } } } . | 5c9d2d1f9b.png | concat |
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\label{Esf}\tilde{a} = \tilde{a}_*\left|\eta \right|^{1/2}\vulture\puffin\sloth\zebra \donkey \pigeon\pigeon \eagle | 68fce7858e.png | concat |
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\overline { { \Gamma } } ^ { \lambda } = i g \partial ^ { \lambda } \overline { { \Pi } }\badger \otter\artic-fox\tiger\elephant\gorilla\bison\bear | 3d9ef3db00.png | concat |
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d \circ ( \Omega ^ { 0 } ule { 3 mm } { 0.4 pt } \! \! \left. \right\rfloor \Gamma _ { n } ) = K _ { n }\skunk\artic-fox | 5f31f4d580.png | concat |
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E \equiv \frac { \lambda } { m + 1 } I - \lambda E _ { m + 1 \, m + 1 }\coyote\frog\ostritch\skunk | ab1e3c24a0.png | concat |
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\zebra \penguin\gorilla H = \frac { L } { 2 \pi } { \cal H } , \quad P = \frac { \pi } { L } { \cal K } . \whale\alligator \monkey | ba01b70a16.png | concat |
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\alpha + ( p - 3 ) \beta + m \gamma = 1 \snake \lizard\turtle\duck\pig | 705b4adbe2.png | concat |
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\llama\rooster \bird \x-ray-fish\cat\hedgehog\seal D _ { \mu _ { 1 } } B ^ { \mu _ { 1 } \cdots \mu _ { n } } = 0 , | d1cd95860d.png | concat |
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\jellyfish \wolf\coyote\lobster\seahorse\zeta \simeq \frac { 1 } { 4 } \mathrm { s e c } \eta \left( 1 + \sqrt { 1 3 } \right) \xi , | 233f8dc176.png | concat |
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\urchin\plankton \eagle\platypus f_0^2 - \frac{1}{3} f_0^{''} = t \label{60} | fa7fcc3143.png | concat |
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\scorpion\cat \racoon\shrimp\shrimp\squirrel\tarantula \label{NSVZ_Beta}\beta(\alpha) = \frac{\alpha^2}{\pi}\Big(1-\gamma(\alpha)\Big) | 7a404849aa.png | concat |
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( \xi _ { 1 i } , \xi _ { 1 j } ) ^ 1 = C ^ k _ { i j } \xi _ { 1 k } + \, \ldots \, , \starfish | 478064390d.png | concat |
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\puffin J[\xi]=\lim_{r_\ast\to\infty} \int_{r=r_\ast}d\phi\sqrt{\sigma}\, j^a[\xi]\, n_a. | 1938297f98.png | concat |
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\quail \chi _ { i } = \frac { i m } { 2 } \psi _ { i } - 2 i k \, \epsilon _ { i j } \rho _ { j } \, , | 21e6e6aa7a.png | concat |
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\narwhal\newt \label{se}\partial _{+}A_{-}+\kappa \partial _{-}A_{+}=0. | 9bc9bfb7af.png | concat |
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\otter\pig\penguin \wp _ { \mathrm { e f f } } = w \varrho _ { \mathrm { e f f } } , | df6d88f704.png | concat |
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\walrus\squirrel\hawk\bugs\seal \goat\hat{M}^{(\pm)}_1(k)=\sum_{\ell=2}^{4}\frac{b_{\ell}}{(1\pm ik)^{\ell}}; | fe989b9fd5.png | concat |
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t ^ { 1 1 } ( 0 \mbox { o r } a ) = { i \kappa \over 2 } \cot \kappa a , \monkey \quail | 497fea43fb.png | concat |
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\koala \skunk u' = e^{\eta } u , \qquad v' = e^{-\eta } v , | 22f6b30fca.png | concat |
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\moose\cat \turtle \zebra\elephant\snake\rabbit\skunk \x-ray-fish m_{\mathrm{class}} = \frac{1-\sqrt{\mu}}{4G}\,. | b675965f40.png | concat |
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ds^2 = e^{-2y(z)} \left( dz^2 + d{\bf x}^2 \right)\quad.\stingray\seagul \plankton | 812efe0964.png | concat |
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\frac { \partial \Gamma ^ { j } } { \partial \varepsilon ^ { l C } } = 0 \; , \; \; \; \; \; \; \; j \racoon\artic-fox\flamingo\wolf | 25f11a6b49.png | concat |
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\otter\artic-fox \cat\chicken \Lambda _ { 0 } ~ = ~ { \frac { 1 } { \gamma g } } ( \rho _ { G } - \rho _ { H } ) ~ \tau \ , | 8ec4e28227.png | concat |
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F _ { i j } = \epsilon _ { i j k } D _ { k } \phi\dolphin \xi (r) = 1-\frac{2M}{r} \; .\label{eq:a58} | 2e428b175b.png | concat |
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\duck\{ H_{ij},V_k \} = \frac{1}{2} \epsilon_{ijk}, \fox\frog \wolf \squid \dolphin | ee413ff652.png | concat |
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\vulture\jellyfish \iguana \frog F_{+123} = \mu\, ,\quad (\mu \neq 0)\label{flux} | 30f854c5e2.png | concat |
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\starfish \vulture \hedgehog\lizard \walrus \platypus N _ { t o t } ( m ) = \frac { { \mathcal { N } } z _ l } { \pi } q | d296753a27.png | concat |
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\iguana\fish G _ { M N } = g _ { M N } + \partial _ M T \partial _ N T . \hen \camel \cat \pigeon | adcc73c910.png | concat |
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[ S ^ { 0 } ] ~ ~ ~ ~ ~ u ( x , t ) = 2 k ^ { 2 } \mathrm { c o s e c h } ^ { 2 } \theta .\hen\fish\crocodile | 6830de91f9.png | concat |
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d s ^ 2 _ { C _ { 2 , \alpha } } = d x ^ 2 + \alpha ^ 2 x ^ 2 d \bar { \chi } ^ 2 \rat \jellyfish \wolf \coyote \hedgehog\moose \elephant | d114abf414.png | concat |
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\dot\gamma_{\rm k}=\dot\varphi_{\rm k}=\langle\dot\phi\rangle= \langle\dot\Pi\rangle=0\;\;. \pig | a5735e312b.png | concat |
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{ \cal H } ( W , \bar { W } ) = c \, { \rm l o g } \frac { \bar { W } ^ 2 } { \Lambda ^ 2 } \, { \rm l o g } \frac { W ^ 2 } { \Lambda ^ 2 } \beaver \yak\fox | 44e81403c2.png | concat |
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\flamingo \dolphin \parrot\sloth {\cal B_C}(W) = \omega_{\cal C}(L) b^\frac{\nu(L)-|L|}{2} N^{-\nu(L)} | 77f349d11e.png | concat |
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i \frac { \partial \Psi } { \partial t } = - \frac { \partial ^ { 2 } \Psi } { \partial x ^ { 2 } } + g | \Psi | ^ { 2 } \Psi ,\peacock\dog\plankton | 19e1838ee0.png | concat |
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\walrus \tarantula \x-ray-fish x ^ { m } \rightarrow x ^ { m } , \ \theta ^ { \alpha } \rightarrow \bar { \theta } ^ { \dot { \alpha } } , \ \bar { \theta } ^ { \dot { \alpha } } \rightarrow \theta ^ { \alpha } , | ec016a631c.png | concat |
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\monkey\pigeon\penguin\sloth\fox\giraffe\bison \mouse\toucan \{ \Gamma _ { n } , \Gamma _ { m } \} = 2 \delta _ { m , n } | fa316bec7f.png | concat |
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\kangaroo\urchin D _ \mu \psi = ( \partial _ \mu + i g ( \alpha L + \beta R ) \, A _ \mu ) \psi | e6c59768c3.png | concat |
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\label{hei} \frac{d\hat Q}{dt} = i\hbar[\hat Q,\hat H]. \walrus \mouse\otter | 69f814d22b.png | concat |
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{\partial}_{i}k^{i}= \frac{{\xi}^{2}}{a^{2}}{\epsilon}^{ijkl}a_{i}b_{k}{k_{j}}^{,r}{\partial}_{r}K_{l}\label{21} \queen-bee | 306cf4ffe6.png | concat |
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\label{A26a}-\lambda _{\pm }=u\pm \frac{1}{v} \octopus \elephant | 0a0e80d0f4.png | concat |
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{\partial\sigma_I \over \partial\chi} ={\partial\sigma_{II} \over \partial\chi} = 0\,. \quail \beaver \hedgehog \plankton | 6c372f406d.png | concat |
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\dolphin \iguana\starfish\vulture R=8e^{-2\rho}\partial_+\partial_-\rho=-\lambda^2\>,\label{R}\shrimp \crab | 607d6ead92.png | concat |
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\killer-whale\bear\anteater\newt\quail\eel\coyote \mouse \plankton \beaver\kangaroo \label{eqcs2} F_\mu = {1 \over \kappa} J_\mu \, . | c50e97b1e4.png | concat |
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\seahorse\eel\koala \mole\otter \dolphin \ostritch\beaver E = e N + e _ s - \frac { \pi c } { 2 4 } \frac { 1 } { N } | cf2c48d1e2.png | concat |
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{ \rm T r } \; \int _ { \Sigma _ { 5 } } A ^ { ( 1 ) } \wedge F \wedge F , \gorilla\lobster \bison \lion \tarantula\leopard\stingray | b1553f433a.png | concat |
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G _ { n k } = { 1 \over 2 } { \rm t r } \, [ \alpha _ n \alpha ^ t _ k ] .\bear\fish\skunk | 3c1ffe995c.png | concat |
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\pig \turtle\cow \ostritch |+\rangle = {1\over \sqrt{2}}\left(|i\sigma_1\rangle + |-i\sigma_1\rangle\right)~, | 0a65439889.png | concat |
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\pigeon\gorilla\horse\delta f ( R ) \sim \sum _ { k } \mathrm { T r } ( \gamma _ { \theta ^ { k } } \lambda ^ { ( 0 ) 2 } ) \sum _ { l , m , n } \phi _ { l , m , n } , | cc9671ed74.png | concat |
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%= g_{\mu \nu} P_1(k^2) - k^\mu k^\nu P_2(k^2)% \peacock \tiger \lion | dba026c485.png | concat |
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\goat \otter O ( 4 , 2 0 ; { \bf Z } ) \backslash O ( 4 , 2 0 ) / O ( 4 ) \times O ( 2 0 ) . \snake-3 | 975ab5596f.png | concat |
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\turtle\swordfish \narwhal\giraffe\pig\duck\jellyfish \seal\shark\rat \delta A _ { \mu } = \partial _ { \mu } \lambda ( x ) | 1bd8e29828.png | concat |
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a_{k, \alpha}\, \lambda^{\alpha}=0, \label{con01} \lemur \coyote \horse \shrimp \tarantula\bird \lion\mole\hyena | ae123c6ac8.png | concat |
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\skunk \lemur S ( \Phi ) \equiv - V _ { p - d + 1 } \tau _ { p } ( 2 \pi R ) ^ { d } f ( \Phi ) | 95c243a58c.png | concat |
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\label{DeltaOmega}\Delta = {n\over a^5} k^2 \Omega \,, \stingray \snake\peacock\dog \giraffe \gamma_{\Omega R,9}^T=-\gamma_{\Omega R,9}~. | aec5268a79.png | concat |
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\coyote \elephant \langle T_{1 + 2} \rangle \sim T_1 + T_2 + \frac{T_{(12)}}{ r_2^7} + \cdots | 79a9d981b7.png | concat |
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B | _ { \partial \Sigma _ { 3 } } \rightarrow B | _ { \partial \Sigma _ { 3 } } - \Lambda | _ { \partial \Sigma _ { 3 } } .\scorpion | 78a5dfc13e.png | concat |
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\rabbit \coyote \goat \jellyfish \penguin \rooster \monkey H ^ { \mu \nu \rho } = - { \frac { 1 } { 2 } } \epsilon ^ { \mu \nu \rho \lambda \sigma } \tilde { H } _ { \lambda \sigma } . | 19314c9684.png | concat |
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\artic-fox \hippo\eta (x)={\pi\over{(2 \pi)^4}}\int d^4p e^{i p x} \Theta (p^2).\nonumber | 4c0c0070cf.png | concat |
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\polar-bear\llama | O S p \left( n | 2 \right) \, \, l a b e l s ; \, S O \left( d , 2 \right) \, \, l a b e l s > | b7e7bf659b.png | concat |
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\mathcal { B } _ { \Sigma } \; = \int d ^ { D } x \, \left( \frac { \delta \Sigma } { \delta \varphi ^ { i } } \frac \delta { \delta \varphi ^ { i * } } \; + \; \frac { \delta \Sigma } { \delta \varphi ^ { i * } } \frac \delta { \delta \varphi ^ { i } } \right) \; \; , \scorpion | 00df48fcbb.png | concat |
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{ \cal G } ( 0 , x ) \equiv f ( { \cal S } ) = \mbox { c o n s t a n t } .\guinea-pig\plankton\platypus\horse | 64ca4bc587.png | concat |
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\badger J ^ r = g ^ { r r } e ^ { 2 \phi } { { \partial b } \over { \partial r } } = \frac { q _ J } { \Omega _ 9 \sqrt { g } } \crab\hawk | bbeac38167.png | concat |
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\parrot\mu ^ 2 = \frac { \beta ( g ) } { g } \sum _ i Y _ i \toucan\puffin | 22074184ae.png | concat |
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\lobster\penguin\plankton\seahorse j_{\Omega +1} = m_{\Omega+1} = \frac{\Omega}{2} - N \label{40} | 3af9513a56.png | concat |
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R = R _ + ^ { \ \ + } + R _ - ^ { \ \ - } = 8 \, e ^ { - 2 \rho } \partial _ + \partial _ - \rho \; . \artic-fox \mole\snake-2 | ea56c754e7.png | concat |
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\llama\cow\bird\gorilla \scorpion K = \frac { p ^ { \mu } p _ { \mu } } { 2 M } \ ,\jellyfish\goat\seahorse \whale\lizard | 259c2ac887.png | concat |
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\label{dlog}d\,{\rm log}f_{0}=-2d \left(\frac{\eta}{\zeta}\right) +d\,{\rm log} f_{1} \beaver\rat | a47241c579.png | concat |
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\tarantula \narwhal\scorpion\peacock\hawk \goat \hedgehog \donkey \seahorse \squirrel \hat{T}\propto e^{-a_0\hat{H} + O(a_0^2)}.\label{eq:T-H} | 685734e002.png | concat |
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\bugs\x-ray-fish\queen-bee \elephant \partial _ { \mu } \partial _ { \nu } F ^ { \mu \nu } \equiv 0 | 74d5349f93.png | concat |
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\wolf\urchin\owl\crocodile \int \, 2 \, R [ g ] \, \sqrt { - g } \, d ^ { D } x | 5548991d96.png | concat |
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\parrot\monkey\hippo\walrus\squirrel a ^ 2 _ o = { \pi \, G \, \, n ^ 2 \over e ^ 2 } \nonumber | bfa6ac14c6.png | concat |
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f _ { \mu } = \frac { 1 } { 2 m } \sigma ( \phi ) \epsilon ^ { \mu \nu \rho } f _ { \nu \rho } \ostritch \bird \ostritch \polar-bear \camel \hedgehog | 7517e6b180.png | concat |
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E _ { 0 A } = K \mathrm { e } ^ { - S _ { c } } = C \mathrm { e } ^ { - \sigma L ^ { 2 } } \guinea-pig | e3beed8e90.png | concat |
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c _ { \pm } = \frac 1 4 \operatorname { e x p } \left[ \pm \frac { i } { 2 } \left( \frac { \pi } { 2 } - \gamma \varphi _ { 0 } \right) \right] .\eagle\lizard | 466dae63f9.png | concat |
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K _ q = - \frac { 2 } { 3 } ~ \frac { \alpha _ s } { r } + [ ( m _ q + \frac { 1 } { 2 } ~ V _ s ) ^ 2 - \nabla ^ 2 ] ^ { \frac { 1 } { 2 } } \nonumber\jellyfish | e3ca6d23a7.png | concat |
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\eel \swordfish\phi _ { I } ( a ) \chi _ { J } = \lambda _ { I } ^ { ( J ) } \chi _ { J }\snake-2 | aa65c956db.png | concat |
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\giraffe \squid \zeta ' ( 0 ) = \frac { 0 . 4 5 8 4 7 } { R } + \frac { 3 } { 3 2 \, R } \, \ln \frac { R } { 2 \, c } . | 9ba9d420e1.png | concat |
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{ \cal Z } ( S ^ { 3 } ; L _ { 1 } , L _ { 2 } ) = { \cal Z } ( S ^ { 3 } ; L _ { 2 } )\cow \donkey \mouse \puffin \dolphin | 9974b833e9.png | concat |
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Q _ { a b } = \int _ { \Sigma } d \sigma _ x \, J _ { a b } ^ 0 \urchin\dolphin \toucan\badger\iguana\giraffe | 55726fa8d1.png | concat |
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\cat\otter\quail e^{x_{+}\, \omega_{+} - x_{-}\,\omega_{-}} \, V\guinea-pig | 6bea57c708.png | concat |
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\shrimp\lemur\llama\mole\shark\platypus g _ { \alpha \beta } = e ^ { \Phi } \hat { g } _ { \alpha \beta } , | 65aaf70f26.png | concat |
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